Non-contact passive ranging system

ABSTRACT

A non-contact passive ranging system wherein a first imager on a platform is focused on a first object and a second imager on the platform is also focused on the first object. The optical path from the first object to the first imager is configured to be shorter than the optical path from the object to the second imager. Processing circuitry is responsive to an output of the first imager and an output of the second imager as relative motion is provided between the platform and the first object and is configured to calculate the distance from the platform to the object.

FIELD OF THE INVENTION

This subject invention relates to distance measuring systems.

BACKGROUND OF THE INVENTION

Numerous distance measuring systems are known in the art and, byextension, so are systems which are able to resolve the motion of anobject. Systems such as sonar, lidar, radar, and the like involve activeemission of energy from a sensor to the object and thus such systems areoften complex, expensive, and power intensive. The processingrequirements underlying such systems are also typically intensive. Also,many prior systems may be fairly slow to acquire range information.

In fields such as robotics and portable navigation systems, fast,inexpensive, and low power ranging systems are desired.

SUMMARY OF THE INVENTION

It is therefore an object of this invention to provide a non-contactranging system which is passive.

It is a further object of this invention to provide such a rangingsystem which does not involve intensive processing requirements.

It is a further object of this invention to provide such a rangingsystem which quickly acquires range information.

It is a further object of this invention to provide such a rangingsystem which is inexpensive.

It is a further object of this invention to provide such a rangingsystem which is low power in operation.

It is a further object of this invention to provide such a rangingsystem which is readily configurable to operate in differentenvironments, for example in robotics, in vehicle based systems, and inportable navigation systems such as helmet or head mounted systems.

It is a further object of this invention to provide such a rangingsystem which is readily extensible to provide complete motion data.

The subject invention results at least in part from the realization thata viable non-contact passive ranging system, in one example, employsoptical motion sensors configured so one is further away from an objectthan the other in which case the object will, to the sensors, appear tomove at two different rates. Since the position of the two sensors isknown, their outputs enable a processor to readily calculate thedistance to the object. By extension, additional pairs of motion sensorsallow the processor to fully calculate the motion of any platform thesensors are attached to.

The subject invention, however, in other embodiments, need not achieveall these objectives and the claims hereof should not be limited tostructures or methods capable of achieving these objectives.

This subject invention features a non-contact passive ranging system.Typically, a first imager on a platform is focused on a first object anda second imager on the platform is also focused on the first object. Theoptical path from the first object to the first imager is designed to beshorter than the optical path from the object to the second imager.Processing circuitry is responsive to the output of the first imager andthe output of the second imager as relative motion is provided betweenthe platform and the first object and is configured to calculate thedistance from the platform to the object.

In one embodiment, each imager is an optical motion sensor eachoutputting a velocity. The platform may be mobile. Also, there may be abeam splitter in the optical path of both the first and second imagers.

In another embodiment, there is a third imager and a fourth imager onthe platform both focused on a second object. The optical path from thesecond object to the third imager is shorter than the optical path fromthe second object to the fourth imager. Now the processing circuitry isalso responsive to an output of the third imager and an output of thefourth imager as relative motion is provided between the platform andthe second object and is configured to calculate the distance from theplatform to the second object. The processing circuitry may be furtherconfigured to calculate the linear velocity of the platform, and alsothe angular velocity of the platform.

In another embodiment, there is a fifth imager and a sixth imager bothfocused on a third object and the optical path from the third object tothe fifth imager is shorter than the optical path from the third objectto the sixth imager. Now the processing circuitry is also responsive toan output of the fifth imager and an output of the sixth imager asrelative motion is provided between the platform and the third objectand is configured to calculate the distance from the platform to thethird object. The processing circuitry can be further configured tocalculate the velocity of the platform in more than one direction andthe angular velocity of the platform about more than one axis.Typically, the optical axes of the fifth and sixth imagers areorthogonal to the optical axes of the third and fourth imagers which areorthogonal to the optical axes of the first and second imagers.

The subject invention also features a method of determining the distancebetween a platform and an object. The method typically includes focusinga first imager on the platform at the object, focusing a second imageron the platform at the same object, and arranging the optical path fromthe first object to the first imager to be shorter than the optical pathfrom the object to the second imager. Relative motion is providedbetween the platform and the object and the distance from the platformto the object is calculated based on reference and sample frames imagedby the first and second imagers. Providing relative motion may includemoving the platform. Typically, the first imager outputs a firstvelocity x_(A) of the platform and the second imager outputs secondvelocity x_(B) of the platform. Calculating the distance h is a functionof x_(A), x_(B) and the position of the first and second imagers on theplatform.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Other objects, features and advantages will occur to those skilled inthe art from the following description of a preferred embodiment and theaccompanying drawings, in which:

FIG. 1 is a highly schematic view showing an example of a non-contactpassive ranging system in accordance with the subject invention;

FIG. 2 is a schematic top view showing a beam splitter in the opticalpath between an object and two imagers in accordance with the subjectinvention;

FIG. 3 is a schematic top view showing another embodiment of anon-contact passive ranging system in accordance with the subjectinvention which is capable of resolving additional motion data;

FIG. 4 is a schematic view showing a configuration of sensors formeasuring motion relative to a plane using five sensors; and

FIG. 5 is a schematic view of a configuration where a sensor is usedtrack a single point on an image.

DETAILED DESCRIPTION OF THE INVENTION

Aside from the preferred embodiment or embodiments disclosed below, thisinvention is capable of other embodiments and of being practiced orbeing carried out in various ways. Thus, it is to be understood that theinvention is not limited in its application to the details ofconstruction and the arrangements of components set forth in thefollowing description or illustrated in the drawings. If only oneembodiment is described herein, the claims hereof are not to be limitedto that embodiment. Moreover, the claims hereof are not to be readrestrictively unless there is clear and convincing evidence manifestinga certain exclusion, restriction, or disclaimer.

FIG. 1 schematically depicts an example of a non-contact passive rangingsystem in accordance with the subject invention. A passive imager B ismounted on platform 10 (a robot or a piece of machinery, for example)and is focused on object 12 (a wall, for example). Imager A is alsolocated on platform 10 and focused on object 12. Sensors A and B areconfigured so the optical path from sensor B to object 12 is shorterthan the optical path from object 12 to sensor A. Typically, sensors Aand B are mounted on platform 10 so they are both focused on the sameimage on a plane. Sensor A is offset along the optical axis of the lenssystem so the optical distance of its image is longer than the opticaldistance of sensor B. Typically this is achieved by using beam splitter20, FIG. 2 in the optical path to provide the same image to bothsensors. The output of each sensor is a delta change that relates to howthe latest image taken by each sensor can be shifted in order to bestmatch a prior image taken by the sensor. These four output quantitiesare combined within processing unit 14, FIG. 1 programmed to determinethe distance to object 12 using equations relating to the geometry ofthe arrangement of the sensors.

In one example, sensors A and B are preferably optical motion sensorscommonly used in optical computer mice. See U.S. Pat. No. 6,995,748incorporated herein by this reference. Further away imager A captures areference frame of object 12 at time t₁ and then a sample frame ofobject 12 at time t₂ as relative motion is provided between platform 10and object 12. Similarly, closer imager B captures a reference frame ofobject 12 at time t₁ and then a sample frame of object 12 at time t₂. Asshown in FIG. 2, assuming both imagers have the same field of view andeach image captured by the closer imager (B) is at least partiallysubsumed by the image captured by the further away imager (A), thecloser imager (B) will output a velocity of platform 10 that is lessthan the velocity of platform 10 output by the further away imager (A).This is because an object moving at a constant velocity will appear toan observer to be moving slower as the distance between the observer andthe object increases.

Processor 14, FIG. 1 (a microprocessor, application specific integratedcircuit, or other equivalent circuitry), is responsive to output X_(A)of imager A and the output X_(B) of imager B and is programmed tocalculate the distance to object 12 as a function of these outputs andthe known relative positions of the imagers. Exemplary electroniccircuitry for controlling imagers A and B and for deriving velocity datais explained in U.S. Pat. No. 6,995,748 referenced above.

As shown in FIG. 3, platform 10 has reference location 30 depicted to bemoving at velocity μ. Thus platform 10 is mobile and object 12 isstationary in this particular example. Imagers A and B on platform 10have different length optical paths to object 12 as discussed above.1_(A) is the distance from imager A to reference location 30 and 1_(B)is the distance from imager B to reference location 30. h₁, the distancefrom reference location 30 to object 12 is unknown but equals:

$\begin{matrix}{h_{1} = \frac{{X_{A}l_{A}} - {X_{B}l_{B}}}{X_{A} - X_{B}}} & (1)\end{matrix}$

where X_(A) and X_(B) are the velocity outputs of imagers A and B,respectively, when reference location 30 is moving with linear velocityμ relative to object 12.

By the addition of imagers C and D both imaging object 32 in a mannersimilar to the way imagers A and B image object 12, the distance h₂ fromreference location 30 to object 32 and also the full motion of platform10 can be resolved by processing circuitry (14, FIG. 1) as follows. q isthe rotation movement of platform 10 about an axis through referencelocation 30. X_(A), X_(B), X_(C), and X_(D) are the velocity outputs ofimagers A, B, C, and D, respectively, as platform 10 moves in thedirection shown at velocity μ thus:

$\begin{matrix}{{X_{A} = {q + \frac{\mu + {l_{A}q}}{h_{1} - l_{A}}}},} & (2) \\{{X_{B} = {q + \left( \frac{\mu + {l_{B}q}}{h_{1} - l_{B}} \right)}},} & (3) \\{{X_{C} = {q + \frac{\left( {{- \mu} + {l_{C}q}} \right)}{h_{2} - l_{C}}}},{and}} & (4) \\{X_{D} = {q + {\frac{{- \mu} + {l_{D}q}}{h_{2} - l_{D}}.}}} & (5)\end{matrix}$

h₁ is then:

$\begin{matrix}{h_{1} = {\frac{{X_{A}l_{A}} - {X_{B}l_{B}}}{X_{A} - X_{B}}.}} & (6)\end{matrix}$

h₂ is:

$\begin{matrix}{h_{2} = {\frac{{X_{C}l_{C}} - {X_{D}l_{D}}}{X_{C} - X_{D}}.}} & (7)\end{matrix}$

q can now be solved:

$\begin{matrix}{{q = \frac{{X_{D}\left( {h_{2} - l_{D}} \right)} + {X_{B}\left( {h_{1} - l_{B}} \right)}}{\left( {h_{2} + h_{1}} \right)}},{or}} & (8) \\{q = {\frac{{X_{C}\left( {h_{2} - l_{C}} \right)} + {X_{B}\left( {h_{1} - l_{B}} \right)}}{\left( {h_{2} + h_{1}} \right)}.}} & (9)\end{matrix}$

μ is:

$\begin{matrix}{{\mu = \frac{{X_{D}\left( {{h_{1}l_{D}} - {h_{2}h_{1}}} \right)} + {X_{B}\left( {{h_{2}h_{1}} - {h_{2}l_{B}}} \right)}}{\left( {h_{2} + h_{1}} \right)}},{or}} & (10) \\{\mu = \frac{{X_{A}\left( {{h_{1}h_{2}} - {h_{2}l_{A}}} \right)} + {X_{C}\left( {{h_{1}l_{C}} - {h_{1}h_{2}}} \right)}}{\left( {h_{2} + h_{1}} \right)}} & (11)\end{matrix}$

By adding another pair of imagers focused on a third object (e.g., thefloor beneath platform 10), additional motion data can be ascertained.

In accordance with the subject invention, no radiation other thanambient illumination or contact is required and the processing time isminimal with low latency and rapid update rates. The subject inventionis not limited to optical sensing devices in the form of the opticalmotion sensors discussed above, however. The optical sensing devicescould be cameras with separate processing units that calculate the frameto frame motion of a video sequence. In accordance with thisconfiguration, it is possible to not only derive a single distance, butto also create a range map which provides readings to all points withinthe field of view of one of the imagers. In this configuration, it isalso possible to derive the motion of the object on which the camerasare mounted.

When cameras are used instead of simple optical motion sensors, thesolution of the depth map of the mutually overlapping portions of thetwo images is possible. With a sufficiently wide field of view and/orpairs of cameras aimed in different directions, it also becomes feasibleto measure the full motion.

The combination of three pairs of such devices in which the optical axisof the three pairs are orthogonal to each other yields the ability tonot only measure the three distances but also to derive the full motionof the object on which the sensors are mounted. In one example, anoptimal combination of five optical navigation sensors arranged withthree in a plane and subtending two orthogonal axes and two morevertically offset allow for the sensing of motion, height, and attituderelative to a reference plane. Such an arrangement might be mounted to aground vehicle such as an automobile and used to measure the sway andtilt of the vehicle in addition to its turn rate and velocity relativeto a plane. Two optical sensing devices could be separated verticallyboth pointing in the same direction but offset slightly horizontally. Inthis arrangement, there will be no optical apparatus to split the imagesand the two devices would be focused on different images but in certainsituations this would still function adequately. The two optical sensingdevices could be separated vertically and offset slightly horizontallybut angled slightly towards each other as well. There could also beother optical apparatus to create the vertical separation between thetwo devices.

There are numerous other possible applications for the subjectinvention. Robotic applications include those requiring image and rangemapping. 3-D model capture in situations involving relative motionbetween a sensor and an object being imaged are also applications. Thesubject invention can be used to sense motion of a moving vehicle ormachine. Altitude sensing for small unmanned aircraft or rotorcraft ispossible as is measurement of motion relative to a flat plane, forexample crane operations, farm equipment navigation, and automobilenavigation.

As shown in FIG. 4, the relative motion of a plane or arrangement ofoptical motion sensors and the plane imaging can be resolved. Smallangles and fast sampling frequency are assumed in the optical sensors.All of the sensors are aligned so that the directions of their outputsare the same. The directions of their X outputs are the same and so arethe direction of their Y outputs. Three sensors (A, B, and C) in a planeare preferably arranged such that the vector from A to B is orthogonalto the vector from A to C. The distance between A and B is equal to thedistance between A and C. Two more sensors are placed in a second planeparallel to the first plane so that the direction from sensor B tosensor E is perpendicular to the first plane and sensor F is similarlyplaced relative to sensor C. The plane being imaged is an unknowndistance from sensor A and angled away from the plane defined by A, B,and C. Sensor A is linearly translating with an unknown velocity in theplane A, B, and C and simultaneously rotating at unknown rates aroundall three axes.

In one example, it can be assumed that l_(C)=i_(B)=l, andl_(F)=l_(E)=l_(h), where l_(h) is the distance from B to E or C to F,and l is the distance from A to B or A to C.

Other definitions are as follows:

x_(A), x_(B), x_(C), x_(E), x_(F) are the X outputs of each opticalsensor and y_(A), y_(B), y_(C), y_(E), y_(F) are the Y output of eachoptical sensor. α is the angle between the vector (B

A) and the projection of that vector onto the image plane, γ is theangle between the vector (C

A) and the projection of that vector onto the image plane, h is thedistance from A to the image plane measured perpendicularly to the plane(A, B, C), h_(B) is the distance from B to the image plane measuredperpendicularly to the plane (A, B, C), and h_(C) is the distance from Cto the image plane measured perpendicularly to the plane (A, B, C). u isthe linear velocity of A in the direction (B

A), v is the linear velocity of A in the direction (C

A), p is the rotational velocity of A about the axis (B

A), q is the rotational velocity of A about the axis (C

A), and r is the rotational velocity of A about the axis (B

A).

Thus,

$\begin{matrix}{{x_{A} = {q + \frac{u}{h}}},} & (12) \\{{x_{B} = {q + \frac{u}{h + {l_{B}\tan \; \alpha}}}},} & (13) \\{{x_{C} = {q + \frac{u + {l_{C}r}}{h - {l_{C}\tan \; \gamma}}}},{and}} & (14) \\{x_{E} = {q + {\frac{u - {l_{E}q}}{h + l_{E} + {l_{B}\tan \; \alpha}}.}}} & (15) \\{y_{A} = {{- p} + \frac{v}{h}}} & (16) \\{{y_{B} = {{- p} + \frac{v - {l_{B}r}}{h + {l_{B}\tan \; \alpha}}}},} & (17) \\{{y_{C} = {{- p} + \frac{v}{h - {l_{C}\tan \; \gamma}}}},{and}} & (18) \\{y_{F} = {{- p} + {\frac{v + {l_{F}p}}{h + l_{F} - {l_{C}\tan \; \gamma}}.}}} & (19)\end{matrix}$

Then,

$\begin{matrix}{{h_{C} = {\frac{x_{F}l_{h}}{x_{C} - x_{F}} = \frac{y_{F}l_{h}}{y_{C} - y_{F}}}},} & (20) \\{{h_{B} = {\frac{x_{E}l_{h}}{x_{B} - x_{E}} = \frac{y_{E}l_{h}}{y_{B} - y_{E}}}},{or}} & (21) \\{\frac{\begin{matrix}{{h_{B}\left( {y_{B} - x_{B}} \right)} +} \\{h_{C}\left( {x_{C} - y_{C}} \right)}\end{matrix}}{\left( {h_{C} - h_{B}} \right)} = {\frac{\left( {{hx}_{A} - {{hx}_{A}x_{B}}} \right)}{\left( {h - h_{B}} \right)} - {\frac{\left( {{hy}_{A} - {h_{C}y_{C}}} \right)}{\left( {h - h_{C}} \right)}.}}} & (22) \\{{{\tan \; (\alpha)} = \frac{h_{B} - h}{l}},} & (23) \\{{{\tan (\gamma)} = \frac{{- h_{C}} + h}{l}},} & (24) \\{{p = \frac{- \left( {{hy}_{A} - {h_{C}y_{C}}} \right)}{\left( {h - h_{C}} \right)}},} & (25) \\{{q = \frac{\left( {{hx}_{A} - {h_{B}x_{B}}} \right)}{\left( {h - h_{B}} \right)}},} & (26) \\{{u = {h_{B}\left( {x_{B} - q} \right)}},} & (27) \\{{v = {h_{C}\left( {y_{C} + p} \right)}},{and}} & (28) \\{r = {\frac{v - {h_{B}\left( {y_{B} + p} \right)}}{l} = {\frac{{h_{C}\left( {x_{C} - q} \right)} - u}{l}.}}} & (29)\end{matrix}$

FIG. 5 and the equations below demonstrate the output of a singleoptical sensor (A) tracking a single point on an image (I) when motionis applied to the sensor in both a linear and rotational sense at anavigated point (N). This can be extended to apply to tracking multiplepoints using a single imager by applying an angular offset of the imageplane equal to the angular location of the image point relative to thecenter of the initial image.

m_(x) is the distance on the focal plane that the image point has moved(output of the optical sensor system), f is the pin-hole equivalentfocal length of the optical lens system employed, l_(A) is the distancefrom the navigated point on the body in motion to the aperture of theoptical system, Δx is the linear motion of the body in motion asmeasured at the navigated point, Δθ is the angular motion of the body inmotion as measure at the navigated point, and h is the distance from thenavigated point to the image point being tracked at the time of theinitial image.

Then,

$\begin{matrix}{{\frac{m_{x}}{f} = {\tan \left( {{\Delta\theta} = {\tan^{- 1}\left( \frac{{\Delta \; x} + {l_{A}\sin \left( {\Delta \; \theta} \right)}}{h - {l_{A}{\cos \left( {\Delta \; \theta} \right)}}} \right)}} \right)}},{and}} & (30) \\{= {\frac{{\tan \left( {\Delta \; \theta} \right)} + \left( \frac{{\Delta \; x} + {l_{A}{\sin \left( {\Delta \; \theta} \right)}}}{h - {l_{A}{\cos \left( {\Delta \; \theta} \right)}}} \right)}{1 - {\left( \frac{{\Delta \; x} + {l_{A}{\sin \left( {\Delta \; \theta} \right)}}}{h - {l_{A}{\cos \left( {\Delta \; \theta} \right)}}} \right){\tan \left( {\Delta \; \theta} \right)}}}.}} & (31)\end{matrix}$

Then, assuming small angles, (i.e. tan θ=θ),

$\begin{matrix}{{\frac{m_{x}}{f} \approx {{\Delta \; \theta} + {\left( \frac{{\Delta \; x} + {l_{A}{\Delta\theta}}}{h - l_{A}} \right)\mspace{14mu} {or}}}},} & (32) \\{\approx {\frac{{\Delta\theta} + \frac{{\Delta \; x} + {l_{A}\Delta \; \theta}}{h - l_{A}}}{1 - {\left( \frac{{\Delta \; x} + {l_{A}\Delta \; \theta}}{h - l_{A}} \right){\Delta\theta}}}.}} & (33)\end{matrix}$

This implies that an assumption of small angles and small distancesholds true for:

$\begin{matrix}{{\left( \frac{{\Delta \; x} + {l_{a}{\Delta\theta}}}{h - l_{A}} \right){\Delta\theta}{\operatorname{<<}1}},{or}} & (34)\end{matrix}$(Δx+l _(A)Δθ)Δθ<<h−l _(A)  (35)

Although specific features of the invention are shown in some drawingsand not in others, this is for convenience only as each feature may becombined with any or all of the other features in accordance with theinvention. The words “including”, “comprising”, “having”, and “with” asused herein are to be interpreted broadly and comprehensively and arenot limited to any physical interconnection. Moreover, any embodimentsdisclosed in the subject application are not to be taken as the onlypossible embodiments. Other embodiments will occur to those skilled inthe art and are within the following claims.

In addition, any amendment presented during the prosecution of thepatent application for this patent is not a disclaimer of any claimelement presented in the application as filed: those skilled in the artcannot reasonably be expected to draft a claim that would literallyencompass all possible equivalents, many equivalents will beunforeseeable at the time of the amendment and are beyond a fairinterpretation of what is to be surrendered (if anything), the rationaleunderlying the amendment may bear no more than a tangential relation tomany equivalents, and/or there are many other reasons the applicant cannot be expected to describe certain insubstantial substitutes for anyclaim element amended.

1. A non-contact passive ranging system comprising: a first imager on aplatform focused on a first object; a second imager on the platform alsofocused on the first object; the optical path from the first object tothe first imager shorter than the optical path from the object to thesecond imager; and processing circuitry responsive to an output of thefirst imager and an output of the second imager as relative motion isprovided between the platform and the first object and configured tocalculate the distance from the platform to the object.
 2. The system ofclaim 1 in which each imager is an optical motion sensor each outputtinga velocity.
 3. The system of claim 1 in which the platform is mobile. 4.The system of claim 1 in which there is a beam splitter in the opticalpath of both the first and second imagers.
 5. The system of claim 1 inwhich there is a third imager and a fourth imager on the platform bothfocused on a second object, the optical path from the second object tothe third imager shorter than the optical path from the second object tothe fourth imager.
 6. The system of claim 5 in which the processingcircuitry is responsive to an output of the third imager and an outputof the fourth imager as relative motion is provided between the platformand the second object and configured to calculate the distance from theplatform to the second object.
 7. The system of claim 6 in which theprocessing circuitry is further configured to calculate the linearvelocity of the platform.
 8. The system of claim 7 in which theprocessing circuitry is further configured to calculate the angularvelocity of the platform.
 9. The system of claim 5 in which there is afifth imager and a sixth imager both focused on a third object, theoptical path from the third object to the fifth imager shorter than theoptical path from the third object to the sixth imager.
 10. The systemof claim 9 in which the processing circuitry is responsive to an outputof the fifth imager and an output of the sixth imager as relative motionis provided between the platform and the third object and configured tocalculate the distance from the platform to the third object.
 11. Thesystem of claim 10 in which the processing circuitry is furtherconfigured to calculate the velocity of the platform in more than onedirection and the angular velocity of the platform about more than oneaxis.
 12. The system of claim 9 in which the optical axes of the fifthand sixth imagers are orthogonal to the optical axes of the third andfourth imagers which are orthogonal to the optical axes of the first andsecond imagers.
 13. A non-contact passive ranging system comprising: afirst optical motion sensor on a platform focused on an object; a secondoptical motion sensor on the platform focused on the same object; theoptical path from the object to the first optical motion sensor shorterthan the optical path from the object to the second optical motionsensor; and processing circuitry responsive to outputs of the first andsecond optical motion sensors as relative motion is provided between theplatform and the object configured to calculate the distance from theplatform to the object.
 14. A method of determining the distance betweena platform and an object, the method comprising: focusing a first imageron the platform at the object; focusing a second imager on the platformat the same object; arranging the optical path from the first object tothe first imager to be shorter than the optical path from the object tothe second imager; providing relative motion between the platform andthe object; and calculating the distance from the platform to the objectbased on reference and sample frames imaged by the first and secondimagers.
 15. The method of claim 14 in which providing relative motionincludes moving the platform.
 16. The method of claim 15 in which thefirst imager outputs a first velocity x_(A) of the platform and thesecond imager outputs second velocity x_(B) of the platform.
 17. Themethod of claim 16 in which calculating the distance h is a function ofx_(A), x_(B) and the position of the first and second imagers on theplatform.